Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#493 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #493 | D43 |
| hypocenter | C43 | D4×D8 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D8×D43 | C2 | semidirect |
| 2. #14583534 | C2 | semidirect |
| 3. #14583132 | C2 | semidirect |
| 4. #14583091 | C2 | semidirect |
| 5. #14583031 | C2 | semidirect |
| 6. C4×D344 | C2 | semidirect |
| 7. C8×D172 | C2 | semidirect |
| 8. C43×#493 | C2 | semidirect |
| 10. C2×D4×D43 | C22 | semidirect |
| 12. C2×#10621882 | C22 | semidirect |
| 14. C2×C8×D43 | C22 | semidirect |
| 16. #13063296 | C22 | semidirect |
| 19. C4×D172 | C22 | semidirect |
| 20. #13063259 | C22 | semidirect |
| 21. C4⋊(C43⋊C8) | C22 | semidirect |
| 22. #13063247 | C22 | semidirect |
| 23. #13063246 | C22 | semidirect |
| 24. (C2×D43)⋊C8 | C22 | semidirect |
| 25. C2×D8×C43 | C22 | semidirect |
| 26. C2×D8×C43 | C22 | semidirect |
| 27. #127×C43 | C22 | semidirect |
| 28. C4×C8×C43 | C22 | semidirect |
| 54. D344 | D4 | semidirect |
| 74. D172 | D8 | semidirect |
| 75. D172 | C2×D4 | semidirect |
| 80. C8×C43 | C2×D4 | semidirect |
| 92. C2×D43 | C2×D8 | semidirect |
| 94. C4×C43 | C2×D8 | semidirect |
| 108. #493 | D43 | semidirect |
| 114. C43 | D4×D8 | semidirect |
| 120. C2×D8 | C2×D43 | semidirect |
| 121. C2×D8 | C2×D43 | semidirect |
| 123. #127 | C2×D43 | semidirect |
| 134. C4×C8 | C2×D43 | semidirect |
| 187. C8 | D4×D43 | semidirect |
| 202. C4 | D8×D43 | semidirect |